Time dependent energy tariffs are a matter of concern to managers in organisations, who need to rethink how to allocate resources to business processes so that they take into account energy costs. However, due to the time-dependent costs, the resource optimisation problem needs to be redesigned. In this paper we formalise the energy-aware resource allocation problem, including time-dependent variable costs; and present a case study in which an auction mechanism is used to find a solution. Our results show how the choice of cost (energy, monetary, or duration) affects the schedules obtained. Abstract: Time dependent energy tariffs are a matter of concern to managers in organisations, who need to rethink how to allocate resources to business processes so that they take into account energy costs. However, due to the time-dependent costs, the resource optimisation problem needs to be redesigned. In this paper we formalise the energy-aware resource allocation problem, including time-dependent variable costs; and present a case study in which an auction mechanism is used to find a solution. Our results show how the choice of cost (energy, monetary, or duration) affects the schedules obtained.